swot hydrology workshop ka-band radar scattering from water and layover issues delwyn moller ernesto...

SWOT Hydrology Workshop

Ka-band Radar Scattering Ka-band Radar Scattering From Water and Layover From Water and Layover

IssuesIssues

Delwyn Moller

Ernesto Rodriguez

Contributions from Daniel Esteban-Fernandez & Michael Durand


Overview and ContextOverview and Context• Instrument simulation for SWOT shows that hydrology requirements

are achievable for nominal operation• Focus on SWOT performance and capabilities in potentially limiting

scenarios:— Establish realistic performance and their dependencies (e.g.

environmental, regional etc).— In limiting scenarios identify possible mitigations, either

operational or algorithmic.— Help specific science interests develop realistic plans for data

interpretation.

• Discuss here the evaluation of two phenomena that can impact the SWOT data product for terrestrial hydrology science:1. Temporal decorrelation of the water surface2. Layover due to topography of the surrounding region


Temporal Decorrelation ImpactTemporal Decorrelation Impact• For a synthetic aperture system the scene must remain correlated over the

aperture synthesis time in order to achieve full resolution.

Note: this does not effect the height error - just the spatial along-track resolution

• Since there is little by way of Ka-band correlation measurements over surface water we collected some initial data from which we were able to derive this quantity

v

€

L = vτ c

ra∝1

L

L1

L2

ra1

ra2


Temporal Coherence ResultsTemporal Coherence Results• Correlation times ranging from 3ms to 44ms were found with the

higher wind measurements producing the shorter correlations. • For a 950km orbit the effect of decorrelation time on the achievable

alongtrack resolution is shown to the right.

- At the shortest anticipated decorrelation times a resolution of ~45m results.

- This may limit our ability to estimate the width (not the height).


A simple test “river” was generated” • 80m wide• No topography (flush with land)• Running at a 55 degree angle to the

radar• 10m (4.4 look) posting along-track, 1

look in range• Realistic thermal and speckle noise• Classification based on power

threshold alone

A Simple Test CaseA Simple Test Case

Classification for Perfect Coherence Classification (c = 7ms) Widening due to Finite (7ms Correlation Time

Algorithm “robustness” issues can occur due to the narrowness of the river (in # of pixels)


Ability to Estimate Width: ResultsAbility to Estimate Width: Results

• Little averaging is required to converge on a mean width estimate

• This is relatively independent of water decorrelation time

€

σwe (∂l) = std

1

∂lw(l)dl

l

l+∂l

∫ ⎛

⎝ ⎜

⎞

⎠ ⎟

Note: We are ultimately limited by finite pixel sizes in estimating width even as the decorrelation -> infinity.

Approaches to correcting for bias shall be investigated next

Width Estimation Variability for an 80m River

Width Estimation Bias due to Decorrelation

Wid

th E

stim

atio

n B

ias(

m)

€

σwe

μw


• Reaches of a few hundred meters are sufficient to average for the estimate of mean width to converge

• Bias is not a function of river width so for very large rivers the percent bias is less

• The next step is to work on an algorithm and sensitivity analysis for correcting the bias

- Radar point-target response can be characterized

- In the mission we may be able to process to different aperture lengths to estimate the correlation time from the azimuth widths

• Temporal decorrelation needs to be better understood and characterized => important to get more experimental data/statistics

Temporal Decorrelation Impact SummaryTemporal Decorrelation Impact Summary


Effects of Topographic Layover: RevisitedEffects of Topographic Layover: Revisited

Layover due to topography occurs when a topographic feature occurs at the same range as the water and thus the energy from both the water and the land occur at the same time and cannot be distinguished


47

45

46

-124 -123 -122

Sample Region for Layover Study: Pacific NorthwestSample Region for Layover Study: Pacific Northwest

Data Sources

DEM: NED 10m posting

Water mask: SRTM water bodies database

• For simplicity we have assumed the spacecraft velocity is constant in longitude.

• For each water pixel, every land pixel who’s range is within the radar range resolution is located

• When layover occurs, the proportional increase of the height error is calculated as follows:

€

lr =1+PLiPw

⎛

⎝ ⎜

⎞

⎠ ⎟

i

∑2

And the relative power ratio accounts for:

1. projected area of the land relative to the water

2. The dot product between the normal to the 2d facet and the incident wave.

3. The relative σ0 between the land and water. Note a 10dB water/land σ0 ratio is assumed at nadir which is then corrected for the local angle of incidence


Layover Simulation ResultsLayover Simulation Results

Note: layover regions are spatially localized and predictable


Layover Statistics Layover Statistics

Height error “scaling” factorHeight error “scaling” factor

• The impact of topographic layover is geographically isolated (and could be predictably removed )

• The magnitude of the additive error is typically very small (>99% of pixels have lr<1.1)


SummarySummary

• Temporal decorrelation of water-bodies can be rapid and consequently limit along-track resolution and our ability to accurately determine the spatial boundaries of the water. However greater statistical knowledge is needed to bound expectations and we will investigate algorithmic approaches to produce a methodology for correction.

• Layover due to topography is usually small and geographically isolated so is not expected to have any significant performance impact.


Backups


Width Finding Algorithm

X axis

Y a

xis

x0 x1

y1

y0

(xc,yc)

w

dx= x1-x0

d y=

y1-

y 0

€

xc,yc( ) = x0 + dx /2,y0 + dy /2( )

tanθ =dydx

w = dx sinθ = dy cosθ

w =dx sinθ( )

2+ dy cosθ( )

2

2

Width finding algorithm: For each i:1. Starting from yi, scan along x until you

find start and end x for intersection. Calculate dx and xc.

2. Starting (xc,yi), find y0 and y1 by scanning up and down. Compute dy and yc.

3. Compute the tangent of the angle, dy/dx. Note that the sign is positive if (y1-yc)/(xc-x0)>0, negative otherwise.

4. Compute the width using the square root formula

5. Save center, width, angle6. Given the direction of the slope, move

to the next neighboring point that is classified water, and repeat. Mark used points as you go.

7. Once a river is completed, restart process with unused water pixels.

8. Smooth center and width along the reach

swot hydrology workshop ka-band radar scattering from water and layover issues delwyn moller ernesto...

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